Inferential Statistics - t test

Inferential Statistics – Hypothesis Testing

Introduction

What is Hypothesis Testing?

?A hypothesis?is an assumption that we intend to check. The approach is very similar to a court trial process in judiciary legislation, where a judge announces the decision made by the jury, stating whether an accused person is guilty or not. There are two types of hypotheses:

• Null hypothesis?(H?)?— the hypothesis that we have by default, or the accepted fact. Usually, it means the absence of an effect. By analogy with the trial process, it is “presumption of innocence” — a legal principle that every person accused of any crime is considered innocent until proven guilty.
• Alternative hypothesis?(H?)?— the hypothesis that we want to test. In other words, the alternative hypothesis will be accepted only if we gather enough evidence to claim that the effect exists.

The null hypothesis and alternative hypothesis are?always?mathematically opposite. The possible outcomes of hypothesis testing:

• Reject the null hypothesis?—a person is found guilty.
• Fail to reject the null hypothesis?— the accused is acquitted.

As broached previously, hypothesis testing is one of the common methodologies in inferential statistics.

Today, all these tests can be simply performed by computers and various tools. Hence, the purpose of this paper is to comprehend how each model works and to avoid excessive focus on calculations and interpretation the results. There are multiple types of hypotheses testing statistical methods, such f-test, t-test, z-test and ANOVA.?

As broached previously, hypothesis testing is one of the common methodologies in inferential statistics.?

Today, all these tests can be simply performed by computers and various tools. Hence, the purpose of this paper is to comprehend how each model works and to avoid excessive focus on calculations and interpretation the results. There are multiple types of hypotheses testing statistical methods, such f-test, t-test, z-test and ANOVA.?

T-test:

There are multiple types of t-tests and the decision to use which one, solely depends on the concept behind the analytics of a data set, the purpose and sample sets.

Here you can briefly see the types and definitions:?

Example:

Assume you have the IQ test score of 6 students from class A and 6 students from class B. Given this, the mean value of IQ scores of samples from class B is higher than class A, but is this true for the overall population of both class? In other words, we tend to see if there is a real difference between the means of IQ scores of class A and class B??

Which one of the t-tests seem to be applicable to this case?

Exactly, an independent two-sample t-test?is the one to go with, since two groups are independent, meaning that students studying in class A, clearly would not be studying in class B.?

Basically,?t-statistic is a signal-to-noise ratio. When we assume that the difference between the two groups is real, we don’t expect that their means are exactly the same. Therefore, the greater the difference in the means, the more we are confident that the populations are not the same.?

In addition, there is one other important measure to consider, which is called the level of significance. It simply refers to the level of the risk we are willing to take for a wrong result or decision, represented usually by (α).

The significance level is the desired probability of rejecting the null hypothesis when it is true. For instance, if a researcher selects α=0.05, it means that he is willing to take a 5% risk of falsely rejecting the null hypothesis. Or, in other words, to take the 5% risk of conviction of an innocent. Statisticians often choose α=0.05, while α=0.01 and α=0.1 are also widely used.

Setting a proper significance level needs thoughtfully ordered factors to be observed:

1.?????Losses in the result of incorrect result

2.?????The prior belief of the researcher while defined the hypotheses: ??H? & H1

3.?????The “Power” of the test

The optimum significance level, power and type of potential error will be covered in next chapter, to fully understand the t-test.?

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